Summary
We study the class of sets with small generalized Kolmogorov complexity. The following results are established: 1. A set has small generalized Kolmogorov complexity if and only if it is “semi-isomorphic” to a tally set. 2. The class of sets with small generalized Kolmogorov complexity is properly included in the class of “self-p-printable” sets. 3. The class of self-p-printable sets is properly included in the class of sets with “selfproducible circuits”. 4. A set S has self-producible circuits if and only if there is a tally set T such that P(T)=P(S). 5. If a set S has self-producible circuits, then NP(S)=NP B(S), where NP B( ) is the restriction of NP( ) studied by Book, Long, and Selman [4]. 6. If a set S is such that NP(S) =NP B(S), then NP(S) \( \subseteq\) P(S⊕SAT).
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Balcázar, J.L., Book, R.V. Sets with small generalized Kolmogorov complexity. Acta Informatica 23, 679–688 (1986). https://doi.org/10.1007/BF00264313
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DOI: https://doi.org/10.1007/BF00264313